Jelikož osobní snaha selhala (Excel se pokaždý řádně rafnul), tak sem zkusil něco najít.

Private Sub Worksheet_Change(ByVal Target As Range)
    SetDateRow Target, "A"
End Sub
 
Sub SetDateRow(Target As Range, Col As String)
    If Target.Cells.Count > 1 Then Exit Sub
    Application.EnableEvents = False
    Cells(Target.Row, Col) = Now()
    Application.EnableEvents = True
    Columns("A").AutoFit
End Sub